This has mirrored my experience attempting to "apply" topology in real world circumstances, off and on since I first studied topology in 2011.
I even hesitate now at the common refrain "real world data approximates a smooth, low dimensional manifold." I want to spend some time really investigating to what extent this claim actually holds for real world data, and to what extent it is distorted by the dimensionality reduction method we apply to natural data sets in order to promote efficiency. But alas, who has the time?
I even hesitate now at the common refrain "real world data approximates a smooth, low dimensional manifold." I want to spend some time really investigating to what extent this claim actually holds for real world data, and to what extent it is distorted by the dimensionality reduction method we apply to natural data sets in order to promote efficiency. But alas, who has the time?